# Ants use math to plan their routes

Eric Hopton for redOrbit.com – Your Universe Online
Ants’ movements seemingly hide or mirror mathematical patterns. If we could tap into their inaudible squeaks they might just be saying to each other “Hey, shall we use Gaussian and Pareto distributions for this one, buddy?”
Authors of a new study found apparently random changes in the direction of the insects followed mathematical patterns – in particular those Gaussian and Pareto distributions.
When ants are plotting their elaborate collective paths to food supplies, they are effectively choosing routes that fit statistical distributions of probability.
The team of mathematicians analyzed the trails of a species of Argentine ant (Linepithema humile, an invasive species in many parts of the world) as the insects “foraged” in a petri dish.
Observing ants
The authors, whose study has been published in the journal Mathematical Biosciences, first observed the ants’ behavior as individuals and then as a collective group. Based on these experiments, they discovered random changes in the direction of the insects followed mathematical patterns.
“To be more specific, they are a mixture of Gaussian and Pareto distributions, two probability functions which are commonly used in statistics, and that in this case dictate how much the ant “turns” at each step and the direction it will travel in,” said María Vela Pérez, researcher at the European University in Madrid and co-author of the study.
The scientists had already verified in previous studies that the “persistence” of ants (their tendency not to change their direction) together with the “reinforcement” occurring in areas which they have already visited are two factors which determine their routes as they forage.
This new data enabled the creation of a model that describes the collective movement of the ants on a surface. The numerical simulations on the computer show the formation of ramified patterns very similar to those observed in the petri dishes during the real experiment with ants.
Applications in small robotics
Apart from their biological interest, these advances could be applied in diverse technological fields. “For example, they could be used to design the coordination of a group of micro-robots or small robots to clean a contaminated area or other tasks,” said Vela Pérez.
“This type of study of the modeling, organization and coordination of the animal behavior is a clear example of multidisciplinary collaboration,” added Pérez.
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